Here, \(\alpha _s\)  is an exponent measured in Fourier space which is equal to \(\alpha _{loc}\)  when \(\alpha _{loc}<1\)  [1]}. For \(\alpha =\alpha _{loc}\) , the scaling behavior described by Eq. (REF ) is the standard Family-Vicsek [2]}. Anomalous scaling has been conjectured, via perturbative arguments, not to be in the asymptotic regime of continuum models which feature local interactions and time-dependent noise [3]}.
